GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 10:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If the average (arithmetic mean) of four positive numbers is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 552
Location: PA
If the average (arithmetic mean) of four positive numbers is  [#permalink]

### Show Tags

01 Dec 2010, 04:24
2
15
00:00

Difficulty:

85% (hard)

Question Stats:

54% (02:15) correct 46% (02:04) wrong based on 323 sessions

### HideShow timer Statistics

If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: Tough DS  [#permalink]

### Show Tags

01 Dec 2010, 06:02
4
2
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

Let's say these 4 positive numbers in ascending order are $$a$$, $$b$$, $$c$$, and $$d$$. Given: $$a+b+c+d=160$$. Question: how many are less than 40? Obviously less than 40 can be only 0 (in case all numbers are 40), 1, 2, or 3 numbers (all 4 can not be less than 40 as in this case their sum won't be to 4*40=160).

(1) The two smallest numbers are identical --> $$a=b$$ --> $$2a+c+d=160$$ --> 0 is out as all numbers are not identical and 1 is also out as 2 smallest are equal and if 1 is less than 40 then another is also, but still two answers are possible: 2 or 3 numbers are less than 40. For example: {20, 20, 50, 50} or {20, 20, 30, 70}. Not sufficient.

(2) The average (arithmetic mean) of the two largest numbers is 50 --> $$c+d=100$$ --> $$a+b=60$$. Again 1, 2, or 3 numbers can be less than 40. For example: {10, 50, 50, 50} or {30, 30, 50, 50} or {30, 30, 30, 70}. Not sufficient.

(1)+(2) As from (1) $$a=b$$ and from (2) $$a+b=60$$ then $$a=b=30$$, so two smallest numbers are 30 and 30: {30, 30, c, d}. But still 2 or 3 numbers can be less than 40: {30, 30, 50, 50} or {30, 30, 35, 65}. Not sufficient.

Answer: E.
_________________
##### General Discussion
Manager
Joined: 30 Aug 2010
Posts: 80
Location: Bangalore, India
Re: Tough DS  [#permalink]

### Show Tags

01 Dec 2010, 05:03
1
1
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

Let the #s be a,b,c,d.

Given a+b+c+d=160

note that the average of the 4 #s to be 40, some #s shud be < 40 and the rest shud be >40 OR all 4 shud be equal to 40

stmnt1: The two smallest numbers are identical.
let us say c and d are the smallest among 4. then, c=d
a+b+2c=160
if c and d are < 40 then 2c<80 then a+b shud be > 80 in which i can have both a and b > 40 or a>40 and b<40....NOT SUFF.

stmnt2: The average (arithmetic mean) of the two largest numbers is 50.

let a and b be the largest #s ==> a+b =100now 100+c+d = 160
==>c+d = 60
we can have both c and d < 40 or one < 40 and other > 40 for the SUM to be 60
NOT SUFF.

1&2
As you can see the above bold case points, both the statements, in a way, are pointing to a single piece of info. hence NOT SUFF.

Answer "E".

Regards,
Murali.
Kudos?
Intern
Joined: 12 Sep 2012
Posts: 25
GMAT 1: 550 Q49 V17
Re: If the average (arithmetic mean) of four positive numbers is  [#permalink]

### Show Tags

12 Oct 2014, 10:17
Bunuel wrote:
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

Let's say these 4 positive numbers in ascending order are $$a$$, $$b$$, $$c$$, and $$d$$. Given: $$a+b+c+d=160$$. Question: how many are less than 40? Obviously less than 40 can be only 0 (in case all numbers are 40), 1, 2, or 3 numbers (all 4 can not be less than 40 as in this case their sum won't be to 4*40=160).

(1) The two smallest numbers are identical --> $$a=b$$ --> $$2a+c+d=160$$ --> 0 is out as all numbers are not identical and 1 is also out as 2 smallest are equal and if 1 is less than 40 then another is also, but still two answers are possible: 2 or 3 numbers are less than 40. For example: {20, 20, 50, 50} or {20, 20, 30, 70}. Not sufficient.

(2) The average (arithmetic mean) of the two largest numbers is 50 --> $$c+d=100$$ --> $$a+b=60$$. Again 1, 2, or 3 numbers can be less than 40. For example: {10, 50, 50, 50} or {30, 30, 50, 50} or {30, 30, 30, 70}. Not sufficient.

(1)+(2) As from (1) $$a=b$$ and from (2) $$a+b=60$$ then $$a=b=30$$, so two smallest numbers are 30 and 30: {30, 30, c, d}. But still 2 or 3 numbers can be less than 40: {30, 30, 50, 50} or {30, 30, 35, 65}. Not sufficient.

Answer: E.

Well, I am little bit confused with the answer. Rather C seems more tempting to me. If we combine both statements then we come to know there two numbers greater than 40 and two numbers less than 40. We can come up with the answer using both the statements. I have interpreted smallest number as less than 40 whereas largest as more than 40. So, {30, 30, 35, 65} cant be present. Kindly rectify me where I went wrong.
Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: If the average (arithmetic mean) of four positive numbers is  [#permalink]

### Show Tags

12 Oct 2014, 11:51
deya wrote:
Bunuel wrote:
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

Let's say these 4 positive numbers in ascending order are $$a$$, $$b$$, $$c$$, and $$d$$. Given: $$a+b+c+d=160$$. Question: how many are less than 40? Obviously less than 40 can be only 0 (in case all numbers are 40), 1, 2, or 3 numbers (all 4 can not be less than 40 as in this case their sum won't be to 4*40=160).

(1) The two smallest numbers are identical --> $$a=b$$ --> $$2a+c+d=160$$ --> 0 is out as all numbers are not identical and 1 is also out as 2 smallest are equal and if 1 is less than 40 then another is also, but still two answers are possible: 2 or 3 numbers are less than 40. For example: {20, 20, 50, 50} or {20, 20, 30, 70}. Not sufficient.

(2) The average (arithmetic mean) of the two largest numbers is 50 --> $$c+d=100$$ --> $$a+b=60$$. Again 1, 2, or 3 numbers can be less than 40. For example: {10, 50, 50, 50} or {30, 30, 50, 50} or {30, 30, 30, 70}. Not sufficient.

(1)+(2) As from (1) $$a=b$$ and from (2) $$a+b=60$$ then $$a=b=30$$, so two smallest numbers are 30 and 30: {30, 30, c, d}. But still 2 or 3 numbers can be less than 40: {30, 30, 50, 50} or {30, 30, 35, 65}. Not sufficient.

Answer: E.

Well, I am little bit confused with the answer. Rather C seems more tempting to me. If we combine both statements then we come to know there two numbers greater than 40 and two numbers less than 40. We can come up with the answer using both the statements. I have interpreted smallest number as less than 40 whereas largest as more than 40. So, {30, 30, 35, 65} cant be present. Kindly rectify me where I went wrong.

How did you come up with the red part?

Also, why is set {30, 30, 35, 65} not valid? The average is 40, the two smallest numbers are identical and the average (arithmetic mean) of the two largest numbers is 50. All requirements are met.
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2492
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If the average (arithmetic mean) of four positive numbers is  [#permalink]

### Show Tags

14 Apr 2016, 18:17
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

in questions like this...i try to plug in values right away...

x+y+w+z=160

1. x=y.
x and y can be 20, w can be 50, and z=70, or it can be x=y=20, w=30, z=90
2 outcomes, not sufficient.

2. y+w+z=150, or x=10. it can be x=10, y=20, w=30, z=100 or
x=10, y=50, w=50, z=50
so alone not sufficient.

1+2
x=10, y=10
we can have:
w=20, z=120
or
w=50, z=90

2 outcomes..the answer is E.
Director
Joined: 24 Nov 2016
Posts: 927
Location: United States
Re: If the average (arithmetic mean) of four positive numbers is  [#permalink]

### Show Tags

05 Nov 2019, 07:20
rxs0005 wrote:
If the average (arithmetic mean) of four positive numbers is 40, how many of the numbers are less than 40?

(1) The two smallest numbers are identical.
(2) The average (arithmetic mean) of the two largest numbers is 50.

n=4; avg=40; sum=160

(1) The two smallest numbers are identical. insufic.
case 1: a,b=30; c,d=50; {30,30,50,50}; {a,b<40}
case 2: a,b,c,d=40; {40,40,40,40}; {0<40}

(2) The average (arithmetic mean) of the two largest numbers is 50. insufic.
case 1: a,b=30; c,d=50; {30,30,50,50}; {a,b<40}
case 2: a,b=30; c=30; d=70; {30,30,30,70}; {a,b,c<40}

(1 & 2) insufic.
case 1: a,b=30; c,d=50; {30,30,50,50}; {a,b<40}
case 2: a,b=30; c=30; d=70; {30,30,30,70}; {a,b,c<40}

Answer (E)
Re: If the average (arithmetic mean) of four positive numbers is   [#permalink] 05 Nov 2019, 07:20
Display posts from previous: Sort by

# If the average (arithmetic mean) of four positive numbers is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne